Non-associative Hilbert scheme and Thom polynomials

2017/12/26 by Maxim Kazarian, Kazarian, Maxim
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1712.09270

openalex publication_date 2017/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Thom polynomial describes the cohomology class Poincaré dual to the locus of particular singularity of a generic holomorphic map. In this paper we derive a closed formula for the generating function of its coefficients. The method is based on a new construction of the embedding space of punctual Hibert scheme that we call the non-associative Hilbert scheme. The efficiency of the method is demonstrated on explicit computation of a number of Thom polynomials, including those associated with singularities of Thom-Boardman types~Σ^i,j, Σ^2,1,1, Σ^2,2,1, and~Σ^2,2,2.

Citations

• Thom polynomials and Schur functions I
• Thom polynomials for maps of curves with isolated singularities
• Thom series of contact singularities

Related

• Thom series of contact singularities
• Thom polynomials. A primer
• On the structure of Thom polynomials of singularities
• Universal polynomials for multi-singularity loci of maps
• Interpolation characterization of higher Thom polynomials